Problem: Simplify; express your answer in exponential form. Assume $p\neq 0, t\neq 0$. $\dfrac{{(p^{5})^{2}}}{{(p^{4}t^{-4})^{-3}}}$
Explanation: To start, try working on the numerator and the denominator independently. In the numerator, we have ${p^{5}}$ to the exponent ${2}$ . Now ${5 \times 2 = 10}$ , so ${(p^{5})^{2} = p^{10}}$ In the denominator, we can use the distributive property of exponents. ${(p^{4}t^{-4})^{-3} = (p^{4})^{-3}(t^{-4})^{-3}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(p^{5})^{2}}}{{(p^{4}t^{-4})^{-3}}} = \dfrac{{p^{10}}}{{p^{-12}t^{12}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{10}}}{{p^{-12}t^{12}}} = \dfrac{{p^{10}}}{{p^{-12}}} \cdot \dfrac{{1}}{{t^{12}}} = p^{{10} - {(-12)}} \cdot t^{- {12}} = p^{22}t^{-12}$.